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CIE 9709 2022 November Paper 12 Q4

A Level / CIE / P1

CIE 9709 2022 Nov Paper 12 Paper · Question 4

题目

Problem

A geometric progression is such that the third term is 1764 and the sum of the second and third terms is 3444.

Find the 50th term.

(4)
题目中文翻译

一个等比数列的第三项为 1764,第二项与第三项的和为 3444。

求第 50 项。

(4)
原卷通用作答要求

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程;仅给出计算器答案而没有过程,不予评分。除非题目另有精度要求,非精确数值答案保留 3 位有效数字,以度为单位的角度保留 1 位小数。

解答

解法一

思路

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从第二、三项之和减去第三项,便得到第二项。两项相除得公比。

答题过程

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The second term is 3444−1764=16803444-1764=1680, so the ratio is 1764/1680=21/201764/1680=21/20. The fiftieth term is 4848 steps after the second term, so it is

 1680(2120)48= 17474.1…≈17500\begin{align*} &\,1680\Big(\frac{21}{20}\Big)^{48}\\ =&\,17474.1\ldots\approx17500 \end{align*}

to three significant figures.